x0 Prediction From Epsilon

Problem

Recover the clean latent from a noisy sample and the predicted noise: x0 = (x_t - sqrt(1 - alpha_bar_t) * eps) / sqrt(alpha_bar_t).

The signature is x0_from_epsilon(x_t, eps, alpha_bar_t). All values are scalars.

Hint

The x0 estimate is the backbone of DDIM-style deterministic samplers.

case 1

in: [1,0,0.5]

expected: 1.4142135624

case 2

in: [0,1,0.25]

expected: -1.7320508076

case 3

in: [2,0.5,0.25]

expected: 3.1339745962

case 4

in: [1,1,1]

expected: 1

Starter codePython

import math
def x0_from_epsilon(x_t, eps, alpha_bar_t):
    # Your code here
    pass

4 test cases · run your code against them in the editor